An Occlusion-Reduced 3D Hierarchical Data Visualization Technique

Reiko Miyazaki, Takayuki ItohOchanomizu University

{reiko, itot}@itolab.is.ocha.ac.jp

AbstractOcclusion is an important problem to be solved for

readability improvement of 3D visualization techniques.This paper presents an occlusion reduction technique forcityscape-style 3D visualization techniques. The paperfirst presents an algorithm for occlusion reduction. It gen-erates bounding boxes of 3D objects on the 2D displayspace, moves them to reduce their overlap, and finally re-versely projects their movements onto the 3D space. Thepaper then presents an application of the algorithm to ourown hierarchical data visualization technique, and a mu-sic browser based on the technique. The paper also showsseveral numerical evaluations that denote the effectivenessof the presented technique.

1 IntroductionLarge-scale visualization techniques became important

due to the explosion of information. Many visualizationworks have focused on efficiency of display usage, becauseoften we would like to look information as much as possi-ble in one display space. Many other works have focusedon interactivity so that users can flexibly explore the infor-mation. 3D information visualization techniques becamealso very interactive due to performance evolution of 3Dgraphics technology. SDM [3] is a typical interactive 3Dinformation visualization system that displays informationby a cityscape representation. In 3D visualization tech-niques we often cause occlusion among objects, and it of-ten prevents the readability of visualization results. ThisOcclusion is an important problem [4] to be solved, to sat-isfy the above requirement by 3D visualization techniques.

The paper presents a technique that reduces occlu-sion for cityscape-style 3D information visualization tech-niques. The paper first presents an algorithm to avoid oc-clusion among 3D objects, by moving bounding boxes ofthe 3D objects in a 2D display space. The algorithm firstconnects the center points of adjacent bounding boxes bygenerating a Delaunay triangular mesh on the 2D space. Itthen moves the bounding boxes to avoid the overlap, byexpanding edges of the triangles. The algorithm attemptsto minimize the sum of distances between the current posi-tions and the positions calculated as the results of the edge

expansion process, and finally obtain good positions of thebounding boxes. It effectively reduce the occlusion of 3Dobjects by reversely projecting the bounding boxes ontothe 3D space and moving the 3D objects according to themovement of the bounding boxes.

The paper then presents an application of the algorithmto our own cityscape-style hierarchical data visualizationtechnique [5]. The hierarchical data visualization tech-nique represents clusters by nested rectangular regions, andleaf-nodes of the hierarchical data by 3D bars. Our imple-mentation generates bounding boxes on the display space,for each 3D bar, or sets of 3D bars in the clusters. It thencalculates the optimal positions of the bounding boxes, re-versely projects them onto the 3D space, and finally movesthe clusters and bars according to the results of the reverseprojection. Here, our implementation causes a trade-offbetween the reduction of occlusion and amount of visibleinformation. 3D bars repulse each other to reduce the oc-clusion, and therefore many of them go outside the displayspace. Consequently, less information is displayed whenocclusion is reduced successfully. We solved this prob-lem by weighting the movement of 3D bars, so that thetechnique can strategically avoid the occlusion around theregion where a user focuses on. This implementation re-alizes the focus and context representation, which clearlydisplays the focused parts without occlusion, and displaysinformation as much as possible in one display space.

We developed an application of the presented technique,called PileView, which represents a set of music soundfiles. We suppose that the music sound files constructa hierarchy based on their metadata (genre, artist name,and truck number). The application represents the files asthumbnail images, and they are piled in a 3D space for eachartist. It then places the set of piles by applying our hier-archical data visualization technique, and moves them toavoid the occlusion. The paper shows numerical evalua-tion (e.g. reduction ratio of occlusion, and ratio of emptyareas) of the presented technique by using PileView.

2 Related WorkIt is often difficult to display large scale statistics data

onto a 2D space. We therefore often represent such data

as a set of 3D bars that are spread onto the 2D space.Such 3D-based representation is enough common to besupported by recent consumer spreadsheet software. Weoften call such representation ”cityscape”, because the 3Dbars look a group of buildings in a city. Occlusion of the3D bars is a serious problem, and several cityscape-styletechniques support interactive mechanism to visualize theinvisible parts of the data on demand [2] [3]. Occlusion re-duction is an important issue to improve the readability ofinitial view of the cityscape-style visualization techniques.

Tree and graph are typical data structures for informa-tion visualization. Actually, we have large and complicatedtree or graph data in our daily life. While several 2D-basedtree or graph visualization techniques have aimed all-in-one display of the whole data [1] [5], interactive 3D in-formation visualization techniques are also useful for suchdata structures. ConeTree [8], InformationCube [7], andH3 [6] are typical famous interactive 3D techniques forvisualizing trees or graphs. Again, such techniques maycause occlusion of 3D objects and degrade the readability,and interactive operations are necessary to visualize the in-visible parts.

The occlusion reduction technique presented in this pa-per is inspired by a technique for interactive layout of smallobjects in a 2D display space [9]. As this technique at-tempts to keep adequate distances among the objects, ourocclusion reduction algorithm also attempts to keep ade-quate distances among 3D objects in the 2D display space.

3 Occlusion ReductionThis section presents the detailed algorithm of our oc-

clusion reduction technique. This section supposes acityscape-style 3D visualization system shown in Figure1(a). The technique effectively moves 3D bars to reduceocclusion, as shown in Figure 1(c).3.1 Bounding Box

Red boxes in Figure 1(a) are bounding boxes that sur-round 3D bars in a display space. The technique movesbounding boxes in the display space to avoid the over-lap. This section describes the technical detail to move thebounding boxes, while Figure 1(b) also shows the techni-cal detail. The technique then reversely projects the movedbounding boxes onto the 3D space, shown as green boxesin Figure 1(c). It finally moves the 3D bars according tothe reserve projection results, and consequently it reducesthe occlusion of the 3D bars. Figure 1(c) shows that thealgorithm successfully reduces the overlap of 3D bars.3.2 Adjustment of positions of bounding boxes

The technique adjusts the positions of bounding boxesin a 2D display space, so that it can reduce the overlap ofthe bounding boxes. Following is the processing flow ofthe adjustment of the positions:

1. Apply Delaunay triangulation to connect the centerpoints of the bounding boxes.

2. Calculate the areas of overlapped regions for pairs ofbounding boxes connected by the edges of the trian-gular mesh.

3. Calculate the best positions of a pair of boundingboxes, if its overlapped area is larger than 0. Here,the technique calculates the best positions that are onthe line expanding the current triangle edge, the pairof bounding boxes touch each other without overlap-ping, and their movement is the smallest. Figure 1(b)shows the calculation of the optimal positions.

4. Minimize the sum of distances between current andbest positions of the bounding boxes. Here, the pro-cess fixes the position of bounding boxes which hasno overlaps with any other bounding boxes.

Let us formulate the step 4 as follows:

argmin{Σi,j | vij − dvij |2 + |(

1n

Σivi

)− c |2} (1)

vij = vi − vj , dvij = dvi − dvj

Here, vi and vj are current positions of two vertices ofa triangle edge. dvi and dvj are their best positions. n isthe number of vertices of Delaunay triangles, which corre-sponds to the number of bounding boxes. c is the positionof the center of the display space. The algorithm calculatesthe positions of the vertices to minimize the value calcu-lated by the formula (1). The former term of the formulaworks to make vertices closer to their best positions, andthe latter term works to prevent to make the occupied spaceunnecessarily larger.

The technique iterates the above process to obtain thebetter results. Our implementation repeats the process upto 10 times.3.3 Reverse projection to 3D space

Finally, the technique reversely projects the boundingboxes moved in the 2D display space described in Sec-tion 3.2. Following is the process to reversely project thebounding boxes, and calculate the new positions of 3Dbars.

1. Let the center point of a moved bounding box in the2D display space as (x′, y′, z′). Here, we supposethat x′ and y′ has been calculated by the process de-scribed in Section 3.2.

2. Acquire the z value at (x′, y′) from the depthbuffer. Our OpenGL-based implementation acquiresby glReadPixels function.

(a) Definition of bounding boxes(drawn as red rectangles)

(b) Positioning of overlap-avoidedbounding boxes

(c) Feedback onto the3D space

Figure 1: Occlusion reduction.

3. Reversely project the position (x′, y′, z′) in the 2Ddisplay space as (x, y, z) in the 3D space. OurOpenGL-based implementation calculates the posi-tion by gluUnProject function.

4 Occlusion-Reduced Hierarchical Data Vi-sualization

This section presents the implementation of our visu-alization technique applying the occlusion reduction al-gorithm, applying our own hierarchical data visualizationtechnique [5].4.1 3D Visualization Supposed in This Paper

Figure 2 shows an example of visualization by our tech-nique. Supposing hierarchical data shown in Figure 2(a),our original hierarchical data visualization technique rep-resents the data as shown in Figure 2(b). The techniquerepresents leaf-nodes of the hierarchical data as icons, andbranch-nodes as nested rectangular regions. The techniqueaims all-in-one display of the leaf-nodes in the whole hier-archical data, rather than interactive navigation of the hier-archy. Though the visualization algorithm is 2D technique,our implementation displays the information as cityscape-style, by assigning heights to icons and drawing them as3D bars.

Figure 2(c) shows PileView, a music browser introducedin the next section. PileView represents hierarchical struc-ture of music contents like cityscape-style visualizationtechniques, by piling up the leaf-nodes.4.2 Processing Flow4.2.1 Step 1: Initial Layout

Our visualization technique represents leaf-nodes of thehierarchical data as 3D bars, and branch-nodes as nestedrectangular regions. The technique places the data itemsbased on a bottom-up layout algorithm. The algorithm firstplaces the sets of 3D bars in the lower hierarchy of the data,and encloses the sets by rectangular borders. It then tightlypacks the sets of rectangular regions, and again encloses

by larger rectangular borders. Repeating the process fromthe lowest to the top of the hierarchy, it places all the dataitems onto the display space.

While placing the 3D bars, this step sorts the 3D bars ineach cluster based on their heights in order. It then placesshort bars closer, and tall bars far, so that it reduces theocclusion of short bars by tall bars.

4.2.2 Step 2: Occlusion Reduction in Focused Regions

After completing the initial layout in Step 1, the techniqueattempts to reduce the occlusion by applying our algorithmdescribed in Section 3.

We suppose that a user is focusing on a part of the vi-sualization result, and usually he/she would like to clearlyvisualize the focused part. The technique supposes that auser is focusing on the rectangular regions that the cursoris pointing. The technique first applies the occlusion re-duction for bars of focused regions, when initial layout iscalculated, or a user moves the cursor. It encloses all barsin the focused regions by bounding boxes, and applied theocclusion reduction algorithm to the bounding boxes, andmoves the bars to reduce the overlap.

4.2.3 Step 3: Occlusion Reduction for All Rectangu-lar Regions

The technique then applies the occlusion reduction for allrectangular regions. It generates bounding boxes for setsof bars of all the rectangular regions, and moves them toreduce the overlap. We had experiments of this two-stepocclusion reduction comparing with simple one-step oc-clusion reduction, and found that the two-step occlusionreduction was much better at the focused regions.

5 PileView: A Music Browser Applying OurVisualization Technique

This section describes the implementation of PileView,which displays a collection of tunes as piled icons. We sup-

Music

Genres Artists Albums Tracks

Music

Genres Artists Albums Tracks

(a) Example of hierarchy (musicmetadata)

(b) Our own hierarchical datavisualization technique

(c) 3D visualizationby PileView

Figure 2: Hierarchical data visualization presented in this paper.

pose the tunes construct hierarchy based on their metadata.This section calls a leaf-node as node, a group of nodespiled up as a tower as pile, and a group of piles enclosedby a rectangular region as frame.

The pile-based representation is useful to reduce the dis-play area occupied by data items comparing with 2D visu-alization techniques. Figures 2(b) and 2(c) show the samedata; however, piled 3D representation in Figure 2(c) drawsicons larger. Pile-based representation reduces the displayarea while it is possible to click each of the piled iconsunless they are occluded. We suppose that the pile-basedrepresentation is useful if the occlusion is effectively re-duced.

Figure 3 (Left) shows an overview of PileView. It dis-plays all the tunes in the input hierarchical data in onedisplay space, and provides a user interface to select ar-bitrary tunes. It overdraws text information (music meta-data) in the upper-left part of the display space. We de-veloped PileView with Visual C++ and OpenGL, and exe-cuted on Thinkpad T60 (Intel Core Duo Processor T25002GHz, RAM 2GB) with Windows XP Service Pack 2.

5.1 Input Data

We developed a program to extract metadata of mu-sic sound files registered in a music browsing softwareiTunes1, using iTunesAPI. Our implementation extractsvarious metadata, including genre name, artist name, al-bum name, track number, link to the music sound file, andlink to the jacket image.

We gathered input data from a set of music sound filesregistered in iTunes of an author, including 5 genres asframes, 39 artists as piles, and 188 tracks as nodes. Wethen constructed the hierarchy of the music sound files ac-cording to the metadata.

5.2 GUI operationThis section calls a frame pointed by a cursor ”focus

frame”. PileView calculates the new positions of piles andframes when the cursor moves and changes focus frames.Consequently, it updates the layout so that it reduces theocclusion among focus frames and their piles. Pileviewsmoothly moves them applying morphing animation, fromthe original positions to the new positions, to avoid the sud-den change of layout.

PileView can assist users to find arbitrary tunes fromlarge number of collections. It starts playing the musicwhen a user clicks a node.

6 EvaluationThis section introduces the results of numerical evalua-

tions of the presented technique. We can evaluate that thetechnique is effective, if it satisfies the following two con-ditions:

• Less occlusion comparing with 3D visualizationwithout applying the occlusion reduction technique.

• Less layout area comparing with 2D visualization byour original hierarchical data visualization technique[5].

The evaluation results in this section show that the tech-nique satisfies the above conditions.6.1 Evaluation Criteria

We numerically evaluated the following three values(e1, e2, e3) described below, and compared the evaluationof three visualization results (v1, v2, v3) shown in Figure4.e1: Ratio of areas of overlapped regions of boundingboxes in focused frames. It is a ratio of total area of over-lapped regions, shown as a black region in Figure 3 (Right),

1iTunes is a trade mark of Apple Inc.

Display area

Window

Overlapped region

Figure 3: (Left) A music browser applying the presented technique. (Right) Bounding boxes.

v1: 2D visualization (by our originaltechnique)

v2: 3D visualization (without occlusionreduction)

v3: 3D visualization (with occlusionreduction)

Figure 4: Visualization results.

against the total area of bounding boxes in focused frames.We can evaluate that occlusion is successfully reduced inthe focused regions when e1 gets lower.e2: Ratio of areas of overlapped regions of all bound-ing boxes. It is a ratio of total area of overlapped regionsagainst the total area of bounding boxes. We can evaluatethat occlusion is totally reduced when e2 gets lower.e3: Ratio of expansion of display area. It is a ratio ofexpansion of the display area, shown as a dotted rectanglein Figure 3 (Right). We can evaluate that all information iscompactly displayed when e3 gets lower.

6.2 Evaluation ResultsTables 1 and 2 show the evaluation results. Here, we

focused five frames f1 to f5 independently while playingwith the 3D visualization with occlusion reduction shownas v3 in Figure 4. Tables 1 shows e1 to e3 values of beforeand after the occlusion reduction, measuring with the fivefocus frames independently. Table 2 shows the compari-son of the three implementations v1 to v3 shown in Figure4. Here, we zoomed up the 2D visualization result, shownas v1 in Figure 4, until the sizes of jacket images in the

display space got almost similar to the other visualizationresults.

6.3 DiscussionTable 1 denotes that the presented technique applied the

occlusion reduction for various focus frames. In our ex-periments, piles are partially overlapped in f1, totally over-lapped in f2, not overlapped in f3 to f5. In any cases, e1and e2 values are decreased after the occlusion reductionprocess. This result denotes that the presented techniqueeffectively reduces the occlusion for various focus frames.

Table 2 denotes that three implementation are numer-ically compared. It denotes that the presented techniquedrastically reduced the occlusion around the focus frames,because e1 value of v3 is much smaller than e1 value ofv2. Also, it denotes that the presented technique totallyreduced the occlusion, because e2 value of v3 is muchsmaller than e2 value of v2. We can evaluate that the pre-sented technique effectively reduces the occlusion from theabove results.

Table 2 also denotes that e3 value of v3 is much smallerthan e3 value of v1. We can evaluate that the presented

Table 1: Comparison between before and after avoidance of occlusion.e1 e2 e3

Frame Before After Before Afterf1 42.69 3.70 47.11 8.70 142.67f2 78.03 20.38 57.78 8.02 173.08

f3 to f5 0.00 0.00 52.60 6.01 156.64Average 60.36 12.04 52.54 6.95 157.13

Table 2: Comparison of visualization techniques.v1 v2 v3

2D visualization 3D visualization 3D visualizationbefore occlusion reduction after occlusion reduction

e1 0.00 60.36 12.04e2 0.00 52.54 6.95e3 2.75 1.00 1.57

technique keeps smaller layout area comparing with 2Dvisualization, even though occlusion reduction process ex-pands the layout area of 3D cityscape-style visualization.

7 Conclusion and Future WorksThe paper presented a technique to reduce the occlu-

sion for cityscape-style 3D visualization techniques. Wefirst presented an algorithm to reduce the occlusion, whichgenerates bounding boxes of 3D objects in the 2D displayspace, and optimizes their movements to effectively reducethe overlap. We then presented the application of the algo-rithm to our own hierarchical data visualization technique,and the implementation of a hierarchical music browserPileView. We also provided the numerical evaluation thatdemonstrated the effectiveness of the presented technique,which totally reduced the occlusion, and kept smaller lay-out area than our 2D visualization technique.

Our potential future work is as follows:

• Reconsideration of shapes of bounding boxes. Wedo not think that box is always the best shape for sur-rounding 3D objects. We would like to implementother efficient shapes (e.g. ellipses) as bounding ob-jects.

• More precise numerical evaluations, calculating theoverlap of icons themselves, not calculating theoverlap of bounding boxes.

• Subjective evaluations with experimental users.

• Implementation and experiments with othercityscape-style 3D visualization techniques.

• Other applications in addition to the music browser.

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